In the prior art, in the field of computer graphics and CADs, an implicit-function representation or a parametric representation using polygons, etc. has been used as means for representing the shape of an object.
A method of modeling an organic object shape by an implicit-function representation is disclosed, for instance, in T. Nishita and E. Nakamae, “A Method for Displaying Metaballs by Using Bézie Clipping,” Proceeding of EUROGRAPHICS, 1994. In this method, a plurality of implicit surfaces, such as meatballs, are combined. In addition, a scheme of generating implicit surfaces by fitting curved surfaces to roughly defined point-group data is proposed in G. Turk and J. F. O'Brien, “Shape Transformation Using Variational Implicit Surface,” Proceeding of SIGGRAPH, 1999.
In these schemes using implicit surfaces, however, it is difficult to represent details of a complex character. If surface data that represents a detailed shape is to be generated, a high computational cost is required.
In recent years, schemes called “level set methods”, wherein implicit surfaces are generated using signed distance functions, have been proposed, for instance, in S. Osher and R. Fedkiw, “Level Set Methods: An Overview and Some Recent Results,” Journal of Computational Physics, Vol. 169, 2001, and D. Enright, S. Marschner and R. Fedkiw, “Animation and Rendering of Complex Water Surface,” Proceeding of SIGGRAPH, 2002. The advantage of using a signed distance function is that shape information can be represented with accuracy. Thus, when fluid animation is to be produced, this scheme is used as a representation method for accurately handling a variation in surface shape of a fluid.
The above prior art, however, merely discloses how to more accurately represent a variation in shape of an object that has a specified simple shape represented by an implicit function. The prior art is silent on a concrete scheme as to how to represent an object by an implicit function. There has been no proposal for a scheme for generally applying an implicit function to not only a simple-shape object but to a complex-shape object.